Communication systems, whether they are used for transmitting analog or digital data, typically employ power amplifiers as part of the signal transmitter. For example, such power amplifiers are used in radio base station transmitters. Unfortunately, such power amplifiers have non-linear amplitude and phase transfer functions. If plotted, the power amplifier's output signal amplitude and phase as a function of the power amplifier's input amplitude would present non-linear curves over a considerable range of the input signal amplitude. For a strong signal with varying amplitude passing through the power amplifier, the non-linear amplitude and phase transfer functions cause distortions. These distortions pose a significant problem, since they cause a higher error vector magnitude (EVM) value of the transmitted signal, which in turn increases the bit error rate at the receiver of the transmitted data.
One way to avoid these non-linearity distortion effects for digital modulation signaling is to use constant envelope type signals, where only the phase is used to represent the data, but this has the drawback of generally providing only a low bit rate as compared to those types of modulation (such as quadrature amplitude modulation (QAM)) that also employ variations in amplitude to represent the data. Consequently, if a higher bit rate of a non-constant amplitude signal modulation scheme is to be obtained, the non-linearities of the power amplifier must be dealt with.
In Orthogonal Frequency Division Multiplexing (OFDM), the information to transmit is modulated onto a large number of equi-distant subcarriers, also referred to as tones. FIG. 1 shows an OFDM frequency spectrum with the subcarrier frequencies f0 . . . fN-1, where N is the total number of subcarriers spanning the available bandwidth. The use of equi-distant subcarriers minimizes interference between information carried by different subcarriers. Because a large number of subcarriers are added together in OFDM to obtain the modulated signal, all with different frequencies and with varying phase angles, amplitude variations occur in the time domain. The interference between these subcarriers, regardless of their modulation schemes, causes peaks and troughs in the time domain of the amplitude of the modulated signal. And as explained above, the non-linearities of the power amplifier are a problem, since they cause a higher error vector magnitude (EVM) value, which in turn increases the bit error rate at the receiver of the transmitted data.
FIG. 2 illustrates in a conceptual way the OFDM modulation principle in which each OFDM symbol is represented in the frequency domain as a complex plane constellation centered at its subcarrier frequency. Consecutive OFDM symbols are separated by a frequency distance Δf. In this example, 4-QAM is used, where each symbol represents two bits, with the four possible value combinations 00, 01, 10, and 11. Each modulating symbol can be understood as a complex-valued vector in the complex symbol plane, having a real (I) and an imaginary (Q) component. Such a vector can alternatively be represented by the combination of its amplitude and its phase angle.
A frequency spectrum signal, like the one shown in FIG. 2, can be regarded as a frequency vector with as many components as there are subcarriers. Each component of the frequency vector is a complex value that represents the modulation of the corresponding subcarrier. An inverse Fourier transform is then performed on the frequency vector to produce a corresponding time vector, which comprises as many components as there are discrete points in time during the time of a symbol. Each component of the time vector is a complex value that represents the signal value at the corresponding point in time. Before transmission, this time-discrete, digital time domain signal is converted to a time-continuous, analog time domain signal.
FIG. 3 illustrates a continuous time domain representation of an example output signal envelope of a multi-carrier transmitter. The inverse Fourier transform in effect creates and adds the time vectors of all the modulated subcarriers into a single time vector. Unfortunately, when many subcarriers, all with different frequencies, are added to obtain the modulated signal, the interference between these frequencies causes in the time domain undesirable amplitude peaks in the modulated signal that produce undesirable distortion at the power amplifier output.
One brute force approach for reducing the effects of such distortions is to reduce the drive level into the amplifier (“backing off”) so that the amplifier output power is considerably below saturation, where the magnitudes of the AM/AM, AM/PM, and IM distortions are tolerable. But this technique is not an option if the amplifier has to be backed off considerably in order to obtain acceptable distortion levels. Backing off the power amplifier tends to reduce the power conversion efficiency of the power amplifier. Additionally, for a given required transmitter output power, a power amplifier operated at a lower efficiency must be larger (and more expensive) than a power amplifier that can be operated at peak efficiency. Also, for a given output power, a lower-efficiency power amplifier requires a more costly power supply and cooling arrangement.
Another distortion compensation approach is to use linearizing circuitry, in which the linearizing can be, e.g., predistortion, Cartesian feedback, feed forward, or any other linearizing principle. For instance, a predistortion circuitry operates on a modulated signal to be amplified by distorting the modulated signal with a calculated inverse of the transfer function of the power amplifier. Both the amplitude and phase transfer functions can be predistorted. Thus, ideally, the predistortion and the power amplifier distortion cancel each other out in the hope of obtaining linear amplification between the input of the linearizing unit and the output of the RF power amplifier. However, the cost of linearizing can be decreased significantly if the peak-to-average power ratio (PAPR) of the signal to be processed can be lowered.
For multi-carrier modulation like OFDM, a high PAPR of an OFDM signal can be decreased using a subcarrier or “tone” reservation technique. Selected subcarriers, instead of carrying payload data, are reserved for PAPR reduction. The payload data is modulated only onto the non-reserved subcarriers. The hope is to assign to the selected subcarriers amplitude and phase values determined to offset the amplitude peaks produced by the payload subcarriers. But the difficulty is providing a practical and cost effective way of calculating suitable amplitude and phase values for the offsetting subcarriers. Although a peak-by-peak reduction in the time domain is possible, that approach requires multiple iterations to achieve satisfactory PAPR reduction.